use warnings;
use strict;
use JSON::PP qw/decode_json/;

# search a data structure recursively for a specific hash key
# and return its "path" as a string if it is found
sub get_path_by_key {
    my ($data, $search_key) = @_;
    # an array of the data items left to search, each being a hash
    # with keys "d" for the data item and "p" for the item's path:
    my @to_search = ( { d=>$data, p=>[] } );
    while (@to_search) {
        # get the item we're currently inspecting:
        my $cur = shift @to_search;
        if ( ref $$cur{d} eq 'ARRAY' ) {
            # if the data item is an array, go through its indices
            for my $i ( 0 .. $#{$$cur{d}} ) {
                # skip any array values that aren't nested data:
                next unless ref $cur->{d}[$i];
                # put each of the array's values on the search list
                push @to_search, { d=>$cur->{d}[$i],
                    # this means the output won't include indices:
                    p=>$$cur{p} };
                    # this would be one way to include indices:
                    #p=>[ @{$$cur{p}}, "[$i]" ] };
            }
        }
        elsif ( ref $$cur{d} eq 'HASH' ) {
            # if the current data item is a hash,
            # first check if it contains the search key:
            if ( exists $cur->{d}{$search_key} ) {
                # this builds the return value string:
                return join '.', @{$$cur{p}}, $search_key;
            }
            # otherwise, go through the hash's keys:
            for my $k ( sort keys %{$$cur{d}} ) {
                # skip any hash values that aren't nested data:
                next unless ref $cur->{d}{$k};
                # put each of the hash's values on the search list
                push @to_search, { d=>$cur->{d}{$k},
                    p=>[ @{$$cur{p}}, $k ] };
            }
        }
    }
    return  # return nothing in case the key isn't found
}

# this is just an idiom to read the whole __DATA__ section:
my $json = do { local $/; <DATA> };
# decode the JSON string into a Perl data structure:
my $data = decode_json($json);
# use our function:
my $path = get_path_by_key($data, 'Obj11AttributesObj1Key1');
print "path=$path\n";

__DATA__
[ {
    "Obj1": [ {
        "Obj11Id": "Id11",
        "Obj11Version": "v1",
        "Obj11Attributes": {
            "Obj11AttributesObj1": {
                "Obj11AttributesObj1Key1": "1",
                "Obj11AttributesObj1Key2": "3"
            },
            "Obj11AttributesObj2": {
                "Obj11AttributesObj2Key1": "9"
            }
        }
    }, {
        "Obj12Id": "Id12",
        "Obj12Version": "v1",
        "Obj12Attributes": {
            "Obj12AttributesObj1": {
                "Obj12AttributesObj1Key1": "2",
                "Obj12AttributesObj1Key2": "4"
            },
            "Obj12AttributesObj2": {
                "Obj12AttributesObj2Key1": "8"
            },
            "Obj12AttributesArray1": [ {
                "Obj12AttributesArray1Obj1Key1": 1
            } ]
        }
    } ]
}, {
    "Obj2": [ {
        "Obj21Id": "Id21",
        "Obj21Version": "v1",
        "Obj21Attributes": {
            "Obj21AttributesObj1": {
                "Obj21AttributesObj1Key1": "3",
                "Obj21AttributesObj1Key2": "5"
            },
            "Obj21AttributesObj2": {
                "Obj21AttributesObj2Key1": "7"
            }
        }
    }, {
        "Obj22Id": "Id22",
        "Obj22Version": "v1",
        "Obj22Attributes": {
            "Obj22AttributesObj1": {
                "Obj22AttributesObj1Key1": "4",
                "Obj22AttributesObj1Key2": "6"
            },
            "Obj22AttributesObj2": {
                "Obj22AttributesObj2Key1": "0"
            },
            "Obj22AttributesArray1": [ {
                "Obj22AttributesArray1Obj1Key1": 1
            } ]
        }
    } ]
} ]